Equity Risk Premium: Expectations Great and Small
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Equity Risk Premium: Equity Risk Premium: Expectations Great and Expectations Great and
SmallSmall
Richard A. Derrig and Elisha D. OrrRichard A. Derrig and Elisha D. OrrBowles SymposiumBowles Symposium
April 2003April 2003
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Equity Risk Premium (ERP)Equity Risk Premium (ERP)
Definition: Definition:
Difference between the market Difference between the market returnreturn
and a risk-free returnand a risk-free return
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US Equity Risk Premia US Equity Risk Premia S&P 500 1926-2002S&P 500 1926-2002
HorizoHorizonn
Equity Equity ReturnReturn
ss
Risk-Risk-Free Free
ReturnReturn
ERPERP
ShortShort 12.20%12.20% 3.83%3.83% 8.37%8.37%InterInter 12.20%12.20% 4.81%4.81% 7.40%7.40%LongLong 12.20%12.20% 5.23%5.23% 6.97%6.97%
Source: Ibbotson Yearbook (2002) and December 2002 Market Report
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Why the ERP is Important Why the ERP is Important for Actuaries ?for Actuaries ?
Universally accepted benchmark Universally accepted benchmark for pricing riskfor pricing risk
Input into simple CAPM and Input into simple CAPM and Fama-French 3-factor modelFama-French 3-factor model
Affects other cost of capital Affects other cost of capital estimates and discount ratesestimates and discount rates
Market value of liabilities Market value of liabilities
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Paper ObjectivesPaper Objectives
Introduction to the ERP PuzzleIntroduction to the ERP Puzzle Types of ERP Types of ERP Time Series AnalysisTime Series Analysis Catalogue ERP Puzzle LiteratureCatalogue ERP Puzzle Literature Selection of an ERPSelection of an ERP SummarySummary
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ERP PuzzleERP Puzzle
Mehra and Prescott (1985): Mehra and Prescott (1985): – Anomalous results when historical Anomalous results when historical
realized ERP compared to asset realized ERP compared to asset pricing theory valuespricing theory values
– Otherwise, must assume risk aversion Otherwise, must assume risk aversion level outside of “reasonable” range level outside of “reasonable” range
Led to literature to solve the “ERP Led to literature to solve the “ERP puzzle”puzzle”
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Literature to Solve the Literature to Solve the PuzzlePuzzle
11stst thread (Behavioral Finance) thread (Behavioral Finance)– New models and assumptions to New models and assumptions to
explain historical dataexplain historical data
22ndnd thread thread– Estimates of the ERP from standard Estimates of the ERP from standard
economic modelseconomic models– Catalogue in Appendix BCatalogue in Appendix B
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ERP TypesERP Types
Geometric vs. arithmeticGeometric vs. arithmetic Short vs. long investment horizonShort vs. long investment horizon Short vs. long run expectationShort vs. long run expectation Unconditional vs. conditional Unconditional vs. conditional US vs. international market data US vs. international market data Data sources and periodsData sources and periods Real vs. nominal returnsReal vs. nominal returns
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ERP using same ERP using same historical data (1926-historical data (1926-
2002)2002)Investment Investment
HorizonHorizonType of Type of AverageAverage
ERP ERP Historical Historical
ReturnReturnShortShort ArithmeticArithmetic 8.4%8.4%ShortShort GeometricGeometric 6.4%6.4%InterInter ArithmeticArithmetic 7.4%7.4%InterInter GeometricGeometric 5.4%5.4%LongLong ArithmeticArithmetic 7.0%7.0%LongLong GeometricGeometric 5.0%5.0%Source: Ibbotson Yearbook (2002) and December 2002 Market
Report
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Converting from Geometric to Converting from Geometric to Arithmetic ReturnsArithmetic Returns
Formula:Formula:AR = GR + var/2,AR = GR + var/2,
var, variance of the return processvar, variance of the return process
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Time Series AnalysisTime Series Analysis
Stationarity AssumptionStationarity Assumption– Supported by ANOVA regressionsSupported by ANOVA regressions– ARIMA model projects future years ARIMA model projects future years
as average of dataas average of data No significant time trendsNo significant time trends Mean of full Ibbotson series and Mean of full Ibbotson series and
subset (1960+) not statistically subset (1960+) not statistically differentdifferent
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Why Different Why Different Estimates ?Estimates ? HistoricalHistorical
– 1926-20021926-2002– 1802-2001 (Earlier period)1802-2001 (Earlier period)
Dividend Growth ModelDividend Growth Model– Next Ten Years + Remainder of 75 Next Ten Years + Remainder of 75
YearsYears– Historical ≠ ExpectedHistorical ≠ Expected– Conditional versus Unconditional Conditional versus Unconditional
expectationsexpectations
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Short-Horizon ERP byShort-Horizon ERP bySub-periodsSub-periods
II IIII IIIIII1802-1802-18701870
1871-1871-19251925
1926-1926-19921992
Stock Stock ReturnsReturns
7.0%7.0% 6.6%6.6% 6.6%6.6%
Short-Short-term term Gov’tsGov’ts
5.1%5.1% 3.2%3.2% 0.5%0.5%
ERPERP 1.9%1.9% 2.8%2.8% 6.1%6.1%Source: Siegel (1994)
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Catalogue of ERP EstimatesCatalogue of ERP Estimates
Social Security Social Security (1999, 2001)(1999, 2001) Puzzle ResearchPuzzle Research
– Campbell and Shiller (2001)Campbell and Shiller (2001)– Arnott and Ryan (2001), Arnott and Arnott and Ryan (2001), Arnott and
Bernstein (2002)Bernstein (2002)– Fama and French (2002)Fama and French (2002)– Ibbotson and Chen (2003)Ibbotson and Chen (2003)– Constantinides (2002)Constantinides (2002)
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Catalogue of ERP Estimates Catalogue of ERP Estimates (Cont.)(Cont.)
Financial Analyst EstimatesFinancial Analyst Estimates– Claus and Thomas (2001)Claus and Thomas (2001)– Harris and Marston (2001)Harris and Marston (2001)
SurveysSurveys– CFOs, Graham and Harvey (2002)CFOs, Graham and Harvey (2002)– Financial economists, Welch (2000 & Financial economists, Welch (2000 &
2001)2001) Behavioral ApproachBehavioral Approach
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The Next 10 YearsThe Next 10 Years Social SecuritySocial Security
– Lower return over next 10 yearsLower return over next 10 years– Remainder of 75 years likely to be similar Remainder of 75 years likely to be similar
to historical returnsto historical returns Campbell and ShillerCampbell and Shiller
– Current P/E and Div/P ratios far from meanCurrent P/E and Div/P ratios far from mean– With mean reversion assumption, dismal With mean reversion assumption, dismal
forecast for next ten yearsforecast for next ten years Market decrease since 1999 is -37.6% Market decrease since 1999 is -37.6%
or or -14.6% annual-14.6% annual
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TIPSTIPSInflation-Indexed Treasury Inflation-Indexed Treasury
SecuritiesSecuritiesMaturitMaturit
yyCoupon Issue Coupon Issue
RateRateYield to Yield to MaturityMaturity
1/111/11 3.5003.500 1.7631.7631/121/12 3.3753.375 1.8311.8317/127/12 3.0003.000 1.8781.8784/284/28 3.6253.625 2.4982.4984/294/29 3.8753.875 2.4902.4904/324/32 3.3753.375 2.4082.408
Source: WSJ 2/24/2003
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Behavioral FinanceBehavioral Finance Benartzi and Thaler (1995)Benartzi and Thaler (1995) Start with prospect theoryStart with prospect theory
– Loss AversionLoss Aversion Add “mental accounting”Add “mental accounting”
– Myopic Loss AversionMyopic Loss Aversion
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Selecting an ERPSelecting an ERP
Rely on past data to forecast the Rely on past data to forecast the futurefuture
OROR Analyze the past and apply Analyze the past and apply
informed judgment as to future informed judgment as to future differencesdifferences
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What You Need To Know What You Need To Know About ERP EstimatesAbout ERP Estimates
Range of estimates Range of estimates – Appendix BAppendix B
Data and terminologyData and terminology Underlying assumptions Underlying assumptions Your independent analysis is Your independent analysis is
required if estimate differs from required if estimate differs from historical averagehistorical average
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Where to Go From HereWhere to Go From Here
Ibbotson and Chen (2003)Ibbotson and Chen (2003)– Appendix CAppendix C– Fundamental components of the Fundamental components of the
historical ERPhistorical ERP– Change estimates based upon good Change estimates based upon good
judgmentjudgment
The puzzle is not yet solved…The puzzle is not yet solved…